The classifier chains algorithm is aimed at solving the multilabel classification problem by composing the labels into a randomized label order. The classification effect of this algorithm depends heavily on whether the label order is optimal. To obtain a better label ordering, the authors propose a multilabel classifier chains algorithm based on a maximum spanning tree and a directed acyclic graph. The algorithm first uses Pearson's correlation coefficient to calculate the correlation between labels and constructs the maximum spanning tree of labels, then calculates the mutual decision difficulty between labels to transform the maximum spanning tree into a directed acyclic graph, and it uses topological ranking to output the optimized label ordering. Finally, the authors use the classifier chains algorithm to train and predict against this label ordering. Experimental comparisons were conducted between the proposed algorithm and other related algorithms on seven datasets, and the proposed algorithm ranked first and second in six evaluation metrics, accounting for 76.2% and 16.7%, respectively. The experimental results demonstrated the effectiveness of the proposed algorithm and affirmed its contribution in exploring and utilizing label-related information.